Question:
If \(f(x) = \dfrac{2x + 3}{3x - 2}\), \( x \neq \dfrac{2}{3} \), then \( f \circ f \) is{
If \(f(x) = \dfrac{2x + 3}{3x - 2}\), \( x \neq \dfrac{2}{3} \), then \( f \circ f \) is{
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If \( f(f(x)) = x \), then the function often exhibits symmetry. Always test \( f(-x) \) to check odd or even nature.
Updated On: Mar 28, 2026
- an even function
- not defined for all \( x \in \mathbb{R} \)
- a constant function
- an odd function
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The Correct Option is D
Solution and Explanation
Step 1: Find \( f(f(x)) \).
\[ f(f(x)) = f\left( \frac{2x+3}{3x-2} \right) \] Step 2: Substitute into the function.
\[ f(f(x)) = \frac{2\left( \frac{2x+3}{3x-2} \right) + 3}{3\left( \frac{2x+3}{3x-2} \right) - 2} \] Step 3: Simplify.
\[ f(f(x)) = \frac{7x}{7} = x \] Step 4: Test for odd function.
\[ f(f(-x)) = -x = -f(f(x)) \] Step 5: Conclusion.
Hence, \( f \circ f \) is an odd function.
\[ f(f(x)) = f\left( \frac{2x+3}{3x-2} \right) \] Step 2: Substitute into the function.
\[ f(f(x)) = \frac{2\left( \frac{2x+3}{3x-2} \right) + 3}{3\left( \frac{2x+3}{3x-2} \right) - 2} \] Step 3: Simplify.
\[ f(f(x)) = \frac{7x}{7} = x \] Step 4: Test for odd function.
\[ f(f(-x)) = -x = -f(f(x)) \] Step 5: Conclusion.
Hence, \( f \circ f \) is an odd function.
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